Graph forms
for C4 [ 256, 50 ] = UG(ATD[256,37])
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On this page are computer-accessible forms for the graph C4[ 256, 50 ] =
UG(ATD[256,37]).
(I) Following is a form readable by MAGMA:
g:=Graph<256|{ {37, 39}, {249, 251}, {248, 250}, {173, 175}, {69, 71}, {45, 47},
{97, 99}, {141, 143}, {1, 2}, {205, 206}, {192, 195}, {160, 163}, {21, 22},
{128, 131}, {1, 5}, {250, 254}, {232, 236}, {59, 63}, {58, 62}, {57, 61}, {3,
7}, {2, 6}, {219, 222}, {234, 239}, {81, 87}, {251, 253}, {218, 220}, {209,
215}, {208, 214}, {27, 28}, {233, 238}, {98, 101}, {112, 119}, {4, 12}, {244,
252}, {215, 223}, {211, 219}, {210, 218}, {180, 188}, {179, 187}, {178, 186},
{177, 185}, {176, 184}, {7, 15}, {6, 14}, {5, 13}, {144, 152}, {145, 153}, {146,
154}, {147, 155}, {148, 156}, {2, 11}, {246, 255}, {65, 72}, {113, 120}, {115,
122}, {3, 9}, {245, 255}, {181, 191}, {86, 92}, {83, 89}, {82, 88}, {117, 127},
{149, 159}, {114, 121}, {4, 8}, {231, 235}, {230, 234}, {229, 233}, {241, 252},
{243, 254}, {16, 30}, {247, 249}, {85, 91}, {84, 90}, {38, 40}, {17, 31}, {70,
73}, {242, 253}, {116, 123}, {5, 21}, {232, 248}, {15, 31}, {8, 24}, {7, 23},
{6, 22}, {230, 247}, {11, 25}, {228, 246}, {66, 80}, {15, 29}, {14, 28}, {32,
51}, {36, 55}, {35, 48}, {13, 25}, {225, 245}, {224, 244}, {32, 53}, {200, 221},
{35, 54}, {33, 52}, {12, 26}, {237, 251}, {227, 245}, {226, 244}, {13, 27}, {34,
53}, {228, 243}, {8, 16}, {175, 183}, {10, 18}, {9, 17}, {109, 117}, {110, 118},
{143, 151}, {203, 210}, {227, 250}, {9, 19}, {236, 246}, {235, 241}, {207, 213},
{206, 212}, {197, 223}, {172, 182}, {140, 150}, {36, 56}, {67, 95}, {42, 55},
{239, 242}, {195, 222}, {193, 220}, {10, 20}, {238, 240}, {171, 181}, {96, 126},
{139, 149}, {142, 144}, {41, 54}, {204, 211}, {194, 221}, {174, 177}, {46, 49},
{111, 112}, {64, 96}, {158, 190}, {157, 189}, {95, 127}, {129, 161}, {130, 162},
{131, 163}, {132, 164}, {133, 165}, {134, 166}, {135, 167}, {136, 168}, {137,
169}, {138, 170}, {139, 171}, {140, 172}, {141, 173}, {142, 174}, {148, 180},
{146, 179}, {28, 62}, {219, 249}, {157, 191}, {95, 125}, {86, 116}, {75, 105},
{74, 104}, {67, 97}, {29, 63}, {132, 166}, {133, 167}, {79, 108}, {137, 170},
{145, 178}, {147, 176}, {24, 60}, {197, 225}, {196, 224}, {90, 126}, {89, 125},
{79, 107}, {78, 106}, {77, 105}, {76, 104}, {71, 99}, {68, 96}, {27, 61}, {199,
225}, {198, 224}, {85, 115}, {68, 98}, {152, 190}, {207, 231}, {14, 39}, {12,
38}, {204, 230}, {201, 227}, {200, 226}, {192, 234}, {78, 100}, {136, 162},
{151, 189}, {31, 52}, {199, 236}, {21, 57}, {223, 243}, {222, 242}, {221, 241},
{220, 240}, {80, 124}, {75, 103}, {74, 102}, {73, 101}, {72, 100}, {23, 59},
{22, 58}, {29, 48}, {201, 228}, {198, 235}, {31, 50}, {11, 37}, {203, 229},
{202, 228}, {30, 49}, {215, 248}, {19, 35}, {73, 121}, {72, 120}, {71, 119},
{70, 118}, {69, 117}, {20, 36}, {91, 106}, {153, 168}, {18, 32}, {65, 115}, {64,
114}, {25, 43}, {19, 33}, {28, 47}, {154, 169}, {24, 44}, {217, 237}, {26, 46},
{25, 45}, {214, 227}, {20, 34}, {217, 239}, {216, 238}, {87, 97}, {77, 123},
{76, 122}, {66, 116}, {26, 44}, {23, 33}, {128, 182}, {129, 183}, {138, 188},
{150, 160}, {92, 107}, {213, 226}, {16, 40}, {208, 232}, {18, 42}, {17, 41},
{94, 103}, {212, 237}, {206, 247}, {156, 165}, {88, 98}, {130, 184}, {131, 185},
{93, 102}, {80, 108}, {82, 110}, {81, 109}, {134, 186}, {135, 187}, {22, 43},
{159, 161}, {155, 164}, {143, 203}, {154, 208}, {175, 229}, {156, 209}, {159,
210}, {62, 112}, {63, 113}, {60, 110}, {61, 111}, {187, 232}, {152, 206}, {191,
233}, {153, 207}, {58, 109}, {177, 230}, {150, 205}, {144, 204}, {186, 231},
{30, 64}, {158, 192}, {33, 65}, {185, 217}, {172, 204}, {171, 203}, {170, 202},
{169, 201}, {168, 200}, {167, 199}, {166, 198}, {165, 197}, {164, 196}, {163,
195}, {162, 194}, {161, 193}, {34, 66}, {62, 95}, {179, 209}, {174, 205}, {39,
67}, {180, 208}, {189, 216}, {190, 219}, {162, 196}, {189, 218}, {190, 217},
{43, 67}, {57, 81}, {56, 80}, {47, 71}, {44, 68}, {50, 91}, {55, 94}, {44, 70},
{49, 90}, {54, 93}, {40, 68}, {43, 69}, {167, 201}, {166, 200}, {59, 85}, {146,
252}, {51, 92}, {183, 216}, {170, 197}, {164, 213}, {187, 202}, {56, 75}, {165,
214}, {160, 211}, {63, 76}, {37, 81}, {39, 83}, {38, 82}, {46, 88}, {182, 192},
{47, 89}, {163, 212}, {48, 72}, {186, 194}, {61, 69}, {55, 79}, {54, 78}, {53,
77}, {52, 76}, {51, 75}, {50, 74}, {49, 73}, {45, 87}, {53, 79}, {52, 78}, {48,
74}, {188, 199}, {40, 84}, {60, 64}, {42, 86}, {41, 85}, {142, 240}, {191, 193},
{184, 198}, {169, 215}, {176, 207}, {124, 252}, {114, 240}, {38, 161}, {84,
220}, {82, 216}, {86, 221}, {113, 253}, {4, 149}, {10, 155}, {12, 151}, {93,
253}, {66, 224}, {70, 238}, {4, 173}, {94, 244}, {20, 184}, {24, 183}, {65,
242}, {3, 182}, {10, 178}, {18, 168}, {77, 241}, {1, 188}, {8, 181}, {7, 185},
{16, 210}, {17, 212}, {58, 255}, {32, 231}, {120, 176}, {121, 177}, {122, 178},
{123, 179}, {124, 180}, {50, 251}, {57, 243}, {94, 148}, {91, 145}, {90, 144},
{127, 181}, {3, 205}, {93, 147}, {92, 146}, {5, 202}, {1, 209}, {37, 245}, {51,
226}, {45, 254}, {56, 235}, {2, 214}, {23, 195}, {11, 223}, {59, 237}, {89,
143}, {88, 142}, {83, 139}, {84, 140}, {117, 173}, {118, 174}, {119, 175}, {9,
211}, {87, 141}, {35, 249}, {112, 171}, {114, 172}, {126, 160}, {34, 194}, {96,
128}, {100, 132}, {104, 136}, {105, 137}, {113, 145}, {115, 147}, {116, 148},
{125, 157}, {126, 158}, {99, 129}, {102, 132}, {103, 133}, {106, 136}, {107,
137}, {110, 140}, {111, 141}, {125, 159}, {100, 130}, {101, 131}, {108, 138},
{109, 139}, {121, 158}, {108, 133}, {6, 236}, {119, 157}, {27, 246}, {42, 196},
{104, 134}, {105, 135}, {36, 213}, {106, 155}, {123, 138}, {29, 239}, {14, 250},
{46, 218}, {21, 225}, {97, 149}, {98, 150}, {99, 151}, {13, 248}, {118, 128},
{30, 233}, {41, 222}, {107, 156}, {15, 247}, {122, 130}, {19, 234}, {124, 135},
{60, 193}, {101, 152}, {103, 154}, {120, 134}, {127, 129}, {26, 229}, {102,
153}, {83, 256}, {111, 256}, {254, 256}, {255, 256} }>;
(II) A more general form is to represent the graph as the orbit of {37, 39}
under the group generated by the following permutations:
a: (2, 5)(6, 13)(7, 9)(8, 12)(11, 21)(14, 27)(15, 19)(16, 26)(17, 23)(18,
20)(22, 25)(24, 38)(29, 35)(30, 46)(31, 33)(32, 36)(34, 42)(37, 57)(39, 61)(40,
44)(41, 59)(45, 58)(47, 62)(50, 65)(51, 56)(53, 55)(54, 63)(60, 82)(64, 88)(66,
86)(67, 69)(70, 84)(71, 95)(72, 74)(73, 90)(76, 78)(77, 94)(80, 92)(83, 111)(87,
109)(89, 112)(91, 115)(93, 113)(96, 98)(97, 117)(99, 127)(100, 104)(101,
126)(102, 120)(103, 105)(106, 122)(107, 108)(114, 142)(118, 140)(119, 125)(121,
144)(123, 148)(124, 146)(128, 150)(130, 136)(131, 160)(132, 134)(133, 137)(135,
154)(138, 156)(139, 141)(143, 171)(145, 147)(149, 173)(151, 181)(152, 158)(153,
176)(155, 178)(159, 175)(161, 183)(164, 186)(165, 170)(167, 169)(168, 184)(172,
174)(177, 204)(179, 180)(182, 205)(185, 211)(187, 208)(188, 209)(189, 191)(192,
206)(193, 216)(194, 196)(195, 212)(198, 200)(199, 215)(202, 214)(210, 229)(213,
231)(217, 219)(218, 233)(220, 238)(221, 224)(222, 237)(223, 225)(226, 235)(227,
228)(234, 247)(236, 248)(239, 249)(241, 244)(242, 251)(243, 245)(246, 250)(254,
255) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (1, 2, 214, 227, 201, 228, 202, 5)(3, 9, 211, 219, 190, 217, 185, 7)(4, 200,
181, 18, 157, 20, 151, 198)(6, 165, 250, 167, 243, 187, 21, 209)(8, 168, 191,
10, 189, 184, 12, 166)(11, 208, 245, 169, 246, 170, 13, 188)(14, 133, 254, 135,
57, 179, 22, 156)(15, 182, 17, 204, 222, 152, 239, 131)(16, 153, 233, 178, 216,
130, 38, 132)(19, 160, 249, 158, 237, 177, 23, 205)(24, 136, 193, 155, 218, 176,
26, 134)(25, 180, 37, 154, 255, 137, 27, 138)(28, 108, 45, 124, 81, 146, 58,
107)(29, 128, 31, 172, 41, 144, 242, 101)(30, 145, 238, 122, 82, 100, 40,
102)(32, 119, 34, 99, 224, 149, 226, 171)(33, 150, 35, 126, 251, 121, 59,
174)(36, 143, 235, 173, 221, 127, 42, 125)(39, 103, 256, 105, 61, 123, 43,
148)(44, 104, 60, 106, 220, 147, 46, 120)(47, 80, 87, 252, 109, 92, 62, 79)(48,
96, 50, 114, 85, 142, 65, 98)(49, 113, 70, 76, 110, 78, 84, 93)(51, 112, 53, 71,
66, 97, 244, 139)(52, 140, 54, 90, 253, 73, 63, 118)(55, 89, 56, 141, 241, 117,
86, 95)(64, 91, 240, 115, 88, 72, 68, 74)(67, 94, 83, 75, 111, 77, 69, 116)(129,
196, 159, 213, 203, 231, 175, 194)(161, 164, 210, 207, 229, 186, 183, 162)(163,
247, 192, 212, 230, 195, 206, 234)(197, 248, 199, 223, 232, 225, 215, 236)
c: (4, 157)(6, 11)(8, 189)(10, 166)(12, 191)(13, 21)(14, 37)(15, 23)(16,
218)(17, 19)(18, 198)(20, 200)(22, 25)(24, 216)(26, 233)(27, 57)(28, 81)(29,
59)(30, 46)(31, 33)(32, 235)(34, 221)(35, 41)(36, 226)(38, 193)(40, 220)(42,
224)(44, 238)(45, 58)(47, 109)(48, 85)(50, 65)(51, 56)(53, 241)(55, 244)(60,
82)(62, 87)(64, 88)(66, 86)(68, 240)(71, 117)(72, 91)(74, 115)(79, 252)(80,
92)(89, 139)(95, 97)(96, 142)(98, 114)(99, 127)(100, 106)(101, 121)(102,
147)(104, 122)(107, 124)(108, 146)(112, 141)(119, 173)(120, 145)(125, 149)(126,
144)(128, 174)(130, 136)(131, 177)(132, 155)(133, 154)(134, 178)(135, 137)(138,
179)(143, 171)(150, 172)(151, 181)(152, 158)(153, 176)(156, 180)(160, 204)(163,
230)(165, 208)(167, 169)(168, 184)(170, 187)(182, 205)(188, 209)(192, 206)(195,
247)(197, 232)(199, 215)(212, 234)(222, 249)(223, 236)(225, 248)(237, 239)(242,
251)(243, 246)(245, 250)(254, 255)
d: (2, 209)(4, 10)(5, 188)(6, 179)(7, 182)(8, 178)(9, 205)(11, 156)(12, 155)(13,
180)(14, 146)(15, 172)(16, 145)(17, 150)(18, 149)(19, 174)(20, 173)(21, 138)(22,
123)(23, 128)(24, 122)(25, 148)(26, 147)(27, 124)(28, 252)(29, 114)(30, 113)(31,
140)(32, 139)(33, 118)(34, 117)(35, 142)(36, 141)(37, 107)(38, 106)(39, 92)(40,
91)(41, 98)(42, 97)(43, 116)(44, 115)(45, 94)(46, 93)(47, 244)(48, 240)(49,
253)(50, 84)(51, 83)(52, 110)(53, 109)(54, 88)(55, 87)(56, 111)(57, 108)(58,
77)(59, 96)(60, 76)(61, 80)(62, 241)(63, 64)(65, 70)(66, 69)(67, 86)(68, 85)(71,
224)(72, 238)(73, 242)(74, 220)(75, 256)(78, 82)(79, 81)(89, 226)(90, 251)(95,
221)(99, 196)(100, 216)(101, 222)(102, 218)(103, 254)(104, 193)(105, 255)(112,
235)(119, 198)(120, 233)(121, 239)(125, 200)(126, 237)(127, 194)(129, 162)(130,
183)(131, 195)(132, 189)(133, 243)(134, 191)(135, 246)(136, 161)(137, 245)(143,
213)(144, 249)(151, 164)(152, 219)(153, 210)(154, 250)(157, 166)(158, 217)(159,
168)(160, 212)(165, 223)(167, 228)(169, 227)(170, 225)(171, 231)(175, 184)(176,
229)(177, 234)(181, 186)(185, 192)(187, 236)(199, 202)(203, 207)(204, 247)(206,
211)(208, 248)(214, 215)
C4[ 256, 50 ]
256
-1 209 188 2 5
-2 11 1 214 6
-3 182 7 205 9
-4 12 149 8 173
-5 1 13 202 21
-6 22 2 14 236
-7 23 3 15 185
-8 24 4 16 181
-9 211 3 17 19
-10 155 178 18 20
-11 2 25 223 37
-12 4 26 38 151
-13 25 5 27 248
-14 6 28 39 250
-15 247 7 29 31
-16 210 40 8 30
-17 212 41 9 31
-18 168 42 10 32
-19 33 35 234 9
-20 34 36 184 10
-21 22 57 5 225
-22 58 6 21 43
-23 33 59 7 195
-24 44 60 183 8
-25 11 45 13 43
-26 44 12 46 229
-27 13 246 28 61
-28 14 47 27 62
-29 15 48 63 239
-30 233 16 49 64
-31 15 17 50 52
-32 231 18 51 53
-33 23 19 52 65
-34 66 194 20 53
-35 48 249 19 54
-36 55 56 213 20
-37 11 245 81 39
-38 12 82 40 161
-39 67 14 37 83
-40 68 16 38 84
-41 222 17 85 54
-42 55 18 86 196
-43 22 67 25 69
-44 24 68 26 70
-45 254 25 47 87
-46 88 26 49 218
-47 45 89 71 28
-48 35 72 29 74
-49 46 90 73 30
-50 91 74 31 251
-51 92 226 75 32
-52 33 78 31 76
-53 77 34 79 32
-54 78 35 93 41
-55 79 36 94 42
-56 36 80 235 75
-57 243 81 61 21
-58 22 255 62 109
-59 23 237 63 85
-60 110 24 193 64
-61 111 57 69 27
-62 112 58 28 95
-63 113 59 29 76
-64 114 60 30 96
-65 33 242 115 72
-66 34 80 224 116
-67 39 95 97 43
-68 44 40 96 98
-69 71 61 117 43
-70 44 73 238 118
-71 99 47 69 119
-72 100 48 65 120
-73 121 101 70 49
-74 102 48 104 50
-75 56 103 105 51
-76 122 104 52 63
-77 123 105 53 241
-78 100 106 52 54
-79 55 107 53 108
-80 66 56 124 108
-81 57 37 87 109
-82 88 110 38 216
-83 89 256 39 139
-84 220 90 40 140
-85 91 59 115 41
-86 221 92 116 42
-87 45 81 97 141
-88 46 82 98 142
-89 143 47 125 83
-90 144 49 126 84
-91 145 50 106 85
-92 146 51 107 86
-93 253 102 147 54
-94 55 244 103 148
-95 67 125 127 62
-96 68 126 128 64
-97 99 67 149 87
-98 88 68 101 150
-99 71 129 151 97
-100 132 78 72 130
-101 73 152 98 131
-102 132 93 74 153
-103 154 133 94 75
-104 134 136 74 76
-105 77 135 137 75
-106 78 155 91 136
-107 79 156 92 137
-108 133 79 80 138
-109 58 81 117 139
-110 60 82 118 140
-111 112 256 61 141
-112 111 171 62 119
-113 253 145 63 120
-114 121 172 64 240
-115 122 147 85 65
-116 66 123 148 86
-117 69 127 173 109
-118 110 70 128 174
-119 112 157 71 175
-120 176 134 113 72
-121 177 114 158 73
-122 178 115 130 76
-123 77 179 116 138
-124 80 135 180 252
-125 89 157 159 95
-126 90 158 160 96
-127 181 95 117 129
-128 182 96 118 131
-129 99 127 161 183
-130 100 122 162 184
-131 101 128 163 185
-132 100 166 102 164
-133 165 167 103 108
-134 166 104 120 186
-135 187 167 124 105
-136 168 104 106 162
-137 169 170 105 107
-138 188 123 170 108
-139 83 149 171 109
-140 110 84 150 172
-141 143 111 173 87
-142 88 144 174 240
-143 89 203 151 141
-144 90 204 152 142
-145 178 91 113 153
-146 154 179 92 252
-147 176 155 93 115
-148 156 180 94 116
-149 4 159 139 97
-150 160 205 140 98
-151 99 143 12 189
-152 144 101 190 206
-153 145 102 168 207
-154 146 103 169 208
-155 147 106 10 164
-156 165 209 148 107
-157 189 125 191 119
-158 121 190 126 192
-159 210 125 149 161
-160 211 126 150 163
-161 38 159 193 129
-162 136 194 130 196
-163 212 160 195 131
-164 132 155 213 196
-165 133 156 214 197
-166 132 198 134 200
-167 133 199 135 201
-168 200 136 18 153
-169 154 201 137 215
-170 202 137 138 197
-171 112 181 203 139
-172 114 182 204 140
-173 4 117 141 175
-174 177 205 118 142
-175 183 173 119 229
-176 147 184 207 120
-177 121 174 185 230
-178 122 145 10 186
-179 187 209 123 146
-180 188 124 148 208
-181 191 127 171 8
-182 3 192 128 172
-183 24 216 129 175
-184 176 198 20 130
-185 177 7 217 131
-186 231 134 178 194
-187 232 135 179 202
-188 1 199 180 138
-189 157 216 151 218
-190 158 217 152 219
-191 233 157 181 193
-192 234 158 182 195
-193 220 191 60 161
-194 34 221 162 186
-195 23 222 192 163
-196 224 162 42 164
-197 165 223 170 225
-198 166 224 235 184
-199 188 167 225 236
-200 166 221 168 226
-201 167 169 227 228
-202 187 5 170 228
-203 143 210 171 229
-204 144 211 172 230
-205 3 150 206 174
-206 212 247 205 152
-207 176 231 213 153
-208 154 232 180 214
-209 1 156 179 215
-210 16 159 203 218
-211 160 204 9 219
-212 17 237 206 163
-213 36 226 207 164
-214 165 2 227 208
-215 209 223 169 248
-216 189 82 183 238
-217 190 237 239 185
-218 220 210 46 189
-219 211 222 190 249
-220 193 84 218 240
-221 200 194 86 241
-222 242 41 195 219
-223 11 243 215 197
-224 66 198 244 196
-225 199 245 21 197
-226 200 244 213 51
-227 201 245 214 250
-228 243 201 202 246
-229 233 26 203 175
-230 177 234 247 204
-231 235 207 32 186
-232 187 236 248 208
-233 191 238 30 229
-234 192 19 239 230
-235 198 231 56 241
-236 199 232 246 6
-237 212 59 217 251
-238 233 70 216 240
-239 242 234 29 217
-240 220 114 238 142
-241 77 221 235 252
-242 253 222 239 65
-243 254 57 223 228
-244 224 94 226 252
-245 255 37 225 227
-246 255 27 236 228
-247 15 249 206 230
-248 232 13 215 250
-249 35 247 251 219
-250 254 14 248 227
-251 253 50 237 249
-252 244 124 146 241
-253 242 113 93 251
-254 45 243 256 250
-255 58 245 256 246
-256 111 254 255 83
0